Cell mapping methods for investigating micro-chaos

Gyebrószki, Gergely and Csernák, Gábor (2014) Cell mapping methods for investigating micro-chaos. In: Investigating Dynamics in Engineering and Applied Science (IDEAS), 2014.07.03.-2014.07.05., Budapest, Hungary.

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Abstract

Micro-chaos is a phenomenon when small amplitude chaotic oscillations are caused by digital effects (sampling, round-off and processing delay). In previous works, various digitally controlled unstable linear mechanical systems were analysed and the corresponding micro-chaos maps were derived. It was proven, that several chaotic attractors coexist in the state space of these maps, and the distance of the farthest attractor from the desired state can be quite large. This is why the phenomenon could be the source of remarkable control error. Cell mapping methods are tools for analysing the global behaviour of nonlinear dynamical systems; determine fixed points, periodic cycles, chaotic attractors and their domain of attraction. This paper shows the application of such methods (Simple Cell Mapping and Generalized Cell Mapping) to investigate micro-chaos maps.

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